Caseback markings

Gooday all. I'm trying to identify a couple of vintage Omegas that I own, and would appreciate some help. First off I have an 18ct gold dress watch bumper from the early 50s (pics attached). I am curious about the Key logo with a digit 1 in the centre. I am sure that someone out there can tell me what this refers to, so PLEASE do. It's intriguing me.

I also have a Seamaster DeVille from the mid 60s (pics also attached) that has a sort of 'shoe' with the digits 353 engraved within. The movement is a 711.
Any help much appreciated.

The marks you reference are Swiss Poincons de Maitre -- i.e., the marks of the watch case maker. The "key" is the "key of Geneva", and is used to identify gold, platinum and palladium watch cases of thickness 0.3mm or greater made in Geneva. The #1 within the key identifies the case maker as Ed. Wenger SA. The "shoe" logo is actually a hammer head, and is used to identify gold, platinum and palladium watch cases made in Switzerland outside Geneva. The "353" within the hammer head identifies the case maker as Stila SA of La Chaux-de-Fonds. Here is a link to additional info on such markings https://www.vintagewatchstraps.com/swisspdm.php. Nice watches, by the way. Cheers!

Thant's fantastic. Thanks for your guidance.